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Zentralblatt MATH Database 1931 2009 c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
 

Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
Zbl 1042.22005
Anandavardhanan, U.K.; Prasad, Dipendra
Distinguished representations for SL(2). (English)
Math. Res. Lett. 10, No. 5-6, 867-878 (2003). ISSN 1073-2780
http://www.mathjournals.org/mrl/
A representation of a group G is said to be distinguished with respect to a subgroup
H of G if it admits a non-trivial H-invariant linear form, i.e., there exists a linear form
on V such that ((h)v) = (v) for all h H and v V.
This work is on distinguished representations of the group G = SL2(E) with respect to
the subgroup H = SL2(F), where E/F is a quadratic extension of p-adic fields. Denote
by HomH(, 1) the space of H-invariant linear forms. The authors classify distinguished
representations and compute the dimension of HomH(, 1). Possible dimensions are 1,
2 and 4, in contrast to the results for (GLn(E), GLn(F)), where the space of invariant
forms is at most one-dimensional. They show that the dimension of HomH(, 1) varies
inside an L-packet similar in spirit to the multiplicity formula for automorphic repre-
sentations due to J.-P. Labesse and R. P. Langlands [Can. J. Math. 31, 726785 (1979;
Zbl 0421.12014)].
Their approach is based on the structure of L-packets and the results for (GL2(E), GL2(F))

  

Source: Anandavardhanan, U. K. - Department of Mathematics, Indian Institute of Technology Bombay

 

Collections: Mathematics